In this paper we discuss several heuristic strategies which allow one to solve the Whitehead minimization problem much faster (on most inputs) than the classical Whitehead algorithm. The mere fact that these strategies work in practice leads to several interesting mathematical conjectures. In particular, we conjecture that the length of most nonminimal elements in a free group can be reduced by a Nielsen automorphism which can be identified by inspecting the structure of the corresponding Whitehead graph.
Publié le : 2005-05-14
Classification:
Whitehead method,
search heuristics,
automorphisms of a free group,
statistical group theory,
clustering,
20F28,
68T05
@article{1120145566,
author = {Haralick, R. M. and Miasnikov, A. D. and Myasnikov, A. G.},
title = {Heuristics for the Whitehead Minimization Problem},
journal = {Experiment. Math.},
volume = {14},
number = {1},
year = {2005},
pages = { 7-14},
language = {en},
url = {http://dml.mathdoc.fr/item/1120145566}
}
Haralick, R. M.; Miasnikov, A. D.; Myasnikov, A. G. Heuristics for the Whitehead Minimization Problem. Experiment. Math., Tome 14 (2005) no. 1, pp. 7-14. http://gdmltest.u-ga.fr/item/1120145566/